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Review

2014

Review

2014

Submodularity is a property of set functions with deep theoretical consequences and far– reaching applications. At first glance…

Highly Cited

2008

Highly Cited

2008

In the Submodular Welfare Problem, m items are to be distributed among n players with utility functions wi: 2[m] → R+. The…

Highly Cited

2007

Highly Cited

2007

Let $f:2^{N} \rightarrow \cal R^{+}$ be a non-decreasing submodular set function, and let $(N,\cal I)$ be a matroid. We consider…

Highly Cited

2001

Highly Cited

2001

This paper presents a combinatorial polynomial-time algorithm for minimizing submodular functions, answering an open question…

Highly Cited

2000

Highly Cited

2000

We give a strongly polynomial-time algorithm minimizing a submodular function f given by a value-giving oracle. The algorithm…

Highly Cited

1982

Highly Cited

1982

AbstractWe consider the problem: min
$$\{ \mathop \Sigma \limits_{j \in s} f_j :z(S) = z(N),S \subseteqq N\} $$
wherez is a…

Highly Cited

1978

Highly Cited

1978

LetN be a finite set andz be a real-valued function defined on the set of subsets ofN that satisfies z(S)+z(T)≥z(S⋃T)+z(S⋂T) for…

Highly Cited

1978

Highly Cited

1978

This paper gives general conditions under which a collection of optimization problems, with the objective function and the…

Highly Cited

1978

Highly Cited

1978

A real-valued function z whose domain is all of the subsets of N = {1,..., n is said to be submodular if zS + zT ≥ zS ∪ T + zS…

Highly Cited

1978

Highly Cited

1978

Given a finite set E and a real valued function f on P(E) (the power set of E) the optimal subset problem (P) is to find S ⊂ E…